Question: Simplify the following expression: $t = \dfrac{q^2 - 6q + 8}{q - 2} $
First factor the polynomial in the numerator. $ q^2 - 6q + 8 = (q - 2)(q - 4) $ So we can rewrite the expression as: $t = \dfrac{(q - 2)(q - 4)}{q - 2} $ We can divide the numerator and denominator by $(q - 2)$ on condition that $q \neq 2$ Therefore $t = q - 4; q \neq 2$